Abstract
We demonstrate how non-simply-laced gauge and flavor symmetries arise in F-theory on spaces with non-isolated singularities. The breaking from a simply-laced symmetry to one that is non-simply-laced is induced by Calabi-Yau complex structure deformation. In all examples the deformation maintains non-isolated singularities but is accompanied by a splitting of an I1 seven-brane that opens new loops in the geometry near a non-abelian seven-brane. The splitting also arises in the moduli space of a probe D3-brane, which upon traversing the new loop experiences a monodromy that acts on 3-7 string junctions on the singular space. The monodromy reduces the symmetry algebra, which is the flavor symmetry of the D3-brane and the gauge symmetry of the seven-brane, to one that is non-simply-laced. A collision of the D3-brane with the seven-brane gives rise to a 4d \( \mathcal{N}=1 \) SCFT with a non-simply-laced flavor symmetry.
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Grassi, A., Halverson, J., Long, C. et al. Non-simply-laced symmetry algebras in F-theory on singular spaces. J. High Energ. Phys. 2018, 129 (2018). https://doi.org/10.1007/JHEP09(2018)129
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DOI: https://doi.org/10.1007/JHEP09(2018)129